Electrical filters have long been used in the processing of electrical signals. In particular, such electrical filters are used to select desired electrical signal frequencies from an input signal by passing the desired signal frequencies, while blocking or attenuating other undesirable electrical signal frequencies. Filters may be classified in some general categories that include low-pass filters, high-pass filters, band-pass filters, and band-stop filters, indicative of the type of frequencies that are selectively passed by the filter. Further, filters can be classified by type, such as Butterworth, Chebyshev, Inverse Chebyshev, and Elliptic, indicative of the type of bandshape frequency response (frequency cutoff characteristics) the filter provides relative to the ideal frequency response.
The type of filter used often depends upon the intended use. In communications applications, band pass and band stop filters are conventionally used in cellular base stations, cell phone handsets, and other telecommunications equipment to filter out or block RF signals in all but one or more predefined bands. Of most particular importance is the frequency range from approximately 500-3,500 MHz. In the United States, there are a number of standard bands used for cellular communications. These include Band 2 (˜1800-1900 MHz), Band 4 (˜1700-2100 MHz), Band 5 (˜800-900 MHz), Band 13 (˜700-800 MHz), and Band 17 (˜700-800 MHz); with other bands emerging.
Microwave filters are generally built using two circuit building blocks: a plurality of resonators, which store energy very efficiently at a resonant frequency (which may be a fundamental resonant frequency f0 or any one of a variety of higher order resonant frequencies f1-fn); and couplings, which couple electromagnetic energy between the resonators to form multiple reflection zeros providing a broader spectral response. For example, a four-resonator filter may include four reflection zeros. The strength of a given coupling is determined by its reactance (i.e., inductance and/or capacitance). The relative strengths of the couplings determine the filter shape, and the topology of the couplings determines whether the filter performs a band-pass or a band-stop function. The resonant frequency f0 is largely determined by the inductance and capacitance of the respective resonator. For conventional filter designs, the frequency at which the filter is active is determined by the resonant frequencies of the resonators that make up the filter. Each resonator must have very low internal resistance to enable the response of the filter to be sharp and highly selective for the reasons discussed above. This requirement for low resistance tends to drive the size and cost of the resonators for a given technology.
The duplexer, a specialized kind of filter is a key component in the front-end of mobile devices. Modern mobile communications devices transmit and receive at the same time (using LTE, WCDMA or CDMA) and use the same antenna. The duplexer separates the transmit signal, which can be up to 0.5 Watt power, from the receive signal, which can be as low as a pico-Watt. The transmit and receive signals are modulated on carriers at different frequencies allowing the duplexer to select them. The duplexer must provide the frequency selection, isolation and low insertion loss in a very small size often only about two millimeters square.
The front-end receive filter preferably takes the form of a sharply defined band-pass filter to eliminate various adverse effects resulting from strong interfering signals at frequencies near the desired received signal frequency. Because of the location of the front-end receiver filter at the antenna input, the insertion loss must be very low so as to not degrade the noise figure. In most filter technologies, achieving a low insertion loss requires a corresponding compromise in filter steepness or selectivity.
In practice, most filters for cell phone handsets are constructed using acoustic resonator technology, such as surface acoustic wave (SAW), bulk acoustic wave (BAW), and film bulk acoustic resonator (FBAR) technologies. The acoustic resonator has two resonances closely spaced in frequency call the “resonance” frequency and the “anti-resonance” frequency (see K. S. Van Dyke, Piezo-Electric Resonator and its Equivalent Network Proc. IRE, Vol. 16, 1928, pp. 742-764). Such acoustic resonators have the advantages of low insertion loss (on the order of 1 dB at the center frequency), compact size, and low cost compared to equivalent inductor/capacitor resonators. For this reason, acoustic resonator implementations are often used for microwave filtering applications in the front-end receive filter of mobile devices. Acoustic resonators are typically arranged in a ladder topology (alternating series and shunt resonators) in order to create band pass filters. Acoustic ladder filters have been very successful for handset applications, with more than a billion units currently sold each year.
The design of modern microwave filters with acoustic resonators requires detailed models to predict the frequency response of the filter. The customary approach is to build an elaborate phenomenological model using all geometrical aspects of each resonator, e.g., pitch, aperture, length, etc. Because commercial acoustic microwave filters must be able to comply with performance requirements over a broad range of temperatures, it is important to be able to model the performance of an acoustic microwave filter design over a relevant temperature range, so that the filter design can be optimized to ensure that, when fabricated, it complies with the performance requirements over that temperature range. Thus, without an accurate model of the acoustic filter for the effects of temperature, the acoustic filter cannot be designed or optimized consistently.
The simplest and most common approach to accurately model an acoustic filter over a temperature range is to uniformly shift the filter response across the entire frequency range by an amount proportional to the temperature. However, measurements of acoustic microwave filters show that this approach neglects the critical fact that the resonant and anti-resonant frequencies shift by different amounts for a given temperature change. When constructed as part of a filter, this not only leads to the center frequency of the passband changing, but also the width of the passband changing. In particular, the change in the resonant frequencies of all the resonators moves the lower-frequency edge of the filter, while the change in the anti-resonant frequencies of all the resonators moves the higher-frequency edge of the filter, but at disproportionate amounts to the resonant frequencies.
For example, referring to FIG. 1, the frequency response of an acoustic microwave filter was measured at −20° C. (dotted line), 25° C. (solid line), and 100° C. (dashed line). As shown, the passband tends to shift to lower frequencies as the temperature increases. Referring now to FIG. 2, the frequency responses of an actual acoustic microwave filter measured at −20° C. and 100° C. (solid lines) can be compared to simulated frequency responses of a corresponding acoustic microwave filter design that have been proportionally shifted in accordance with the two temperatures (dashed lines). It can be readily seen that, when the left sides of the passbands of the simulated frequency responses at −20° C. and 100° C. are respectively aligned with the left sides of the passbands of the actual frequency responses at −20° C. and 100° C., the right sides of the passbands are not aligned, evidencing the fact that the passband not only shifts as the temperature changes, the passband also distorts as the temperature changes. Therefore, this simple approach incorrectly predicts a bandwidth unchanged by temperature.
A more sophisticated approach to modeling the effects of temperature is to characterize the individual resonators that make up a filter over a range of temperatures. Each model uses a certain number of parameters, which will vary with temperature. Using basic physical knowledge, one can predict how each of these parameters will change as the temperature changes. The response of the resonator is captured with a sort of analytical model, e.g., Butterworth-van Dyke or Coupling-of-Modes (see A. Loseu and J. Rao, 2010 IEEE International Ultrasonics Symposium Proceedings, pp. 1302-1306). However, with as many parameters as are afforded in such a model, it is difficult to find a consistently predictive model. In addition, the construction of such a model is time consuming and onerous. Furthermore, the model may even be misleading, since the important frequency response of each resonator depends sensitively on the surrounding elements when embedded in a filter. Thus, the primary difficulty with this sophisticated method is the faithful translation of the isolated resonator measurements to the same resonator's response once embedded in a filter or duplexer.
There, thus, remains a need to provide an improved method for modeling acoustic microwave filters over a temperature range.